We present a detailed study of the production of a high transverse-momentum lepton pair at hadron colliders, which includes the exact order alpha electroweak corrections properly matched with leading logarithmic effects due to multiple photon emission, as required by the experiments at the Fermilab Tevatron and the CERN LHC. Numerical results for the relevant observables of single Z-boson production at hadron colliders are presented. The impact of the radiative corrections is discussed in detail. The presence in the proton of a photon density is considered and the effects of the photon-induced partonic subprocesses are analyzed. The calculation has been implemented in the new version of the event generator HORACE, which is available for precision simulations of the neutral and charged current Drell-Yan processes.